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-please answer with five decimal places. Use the intermediate value theorem to d

ID: 2840872 • Letter: #

Question

-please answer with five decimal places.

Use the intermediate value theorem to determine whether the function f(x) = x 3 + 6x - 8 has a root or not between x = 1 and x = 2. If yes, then find the root to five decimal places. Does the given function have a root between the interval [1, 2]? If yes, then find the root. Choose the correct answer below. No, the given function has no root between [1,2]. Yes, the given function has a root between [1,2] and the root is (Type an integer or decimal rounded to five decimal places as needed.)

Explanation / Answer

to cut through the chase, the root will be: 1.10715


Now to get it is he hard part. You have to start with 1 and 1.5 as borders. If the root lies within 1.5 and 1, you narrow the border by choosing 1.25 and 1 or 1.25 and 1.5. Ifthe root doesn't lie within 1.5 and 1, it must be between 1.5 and 2. So you try 1.75 and 2 next. As you can see, as we go along the decimial points in the border increase. You have to keep doin this until you reach 5 decimal places. There is an easier iteration to do this, but you question specifies which process to use. I used the iteration because it is more efficient. However, the answer is the same. Hope this helps.